Logarithms 2

$12\log12 = 3a\log3 + 2a\log8$

$\rightarrow 12\log12 = 3a\log3 + 6a\log2$

$\rightarrow 12\log12 = 3a\log3 + 3a\log4$

$\rightarrow 12\log12 = 3a\log12$

$\rightarrow 12 = 3a ------------------ (\log12 \not = 0 )$

$\rightarrow a = \boxed{4}$

$12\log { 12 } =12\times \left( \log { 3 } \times \log { 4 } \right)$

$\rightarrow 12\log { 3 } +12\log { 4 } =3a\log { 3 } + 2a\log { 8 }$

$\rightarrow \left( 12-3a \right) \log { 3 } =\left( 6a-24 \right) \log { 2 }$

Because $f\left( a \right) =\left( 12-3a \right) \log { 3 }$ is monotonically decreasing function and $g\left( a \right) =\left( 6a-24 \right) \log { 2 }$ is monotonically increasing function

So there is only 1 unknown in this equation.

Please draw 2 graphs of f(x) and g(x) and look at these graphs: The answer is a = 4

Hey yo,

as for 12 log 12 = 3a log 3 + 2a log 8

log 12^(12) = log ^(3a) + log 8^(2a)

log 12^(12) = log [ 3^(3a) x 8^(2a)]

12^(12) = 3^(3a) x 8^(2a)

(3 x 4)^12 = 3^(3a) x 8^(2a)

[3^(12)][4^(12)] = 3^(3a) x 8^(2a)

by comparison,

3^(3a) = 3^(12)

3a = 12

a = 12/3 = 4

or

4^(12) = 8^(2a)

2^(24) = 2^(6a)

6a = 24

a = 4

therefore,the answer is a = 4 ,

thanks...

12^12 = 3^3a . 8^2a --> 3^12. 2^24 = 3^3a . 2^6a --> So, a is 4.